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Review Problems
10-72 Steam at a saturation temperature of Tsat = 40(C condenses on the
outside of a thin horizontal tube. Heat is transferred to the cooling water
that enters the tube at 25(C and exits at 35(C. The rate of condensation of
steam, the average overall heat transfer coefficient, and the tube length
are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The tube can be taken
to be isothermal at the bulk mean fluid temperature in the evaluation of
the condensation heat transfer coefficient. 3 Liquid flow through the tube
is fully developed. 4 The thickness and the thermal resistance of the tube
is negligible.
Properties The properties of water at the saturation temperature of 40(C
are hfg = 2407(103 J/kg and (v = 0.05 kg/m3. The properties of liquid water
at the film temperature of (50 + 20)/2 = 35(C and at the bulk fluid
temperature of (25 + 35)/2 = 30(C are (Table A-9),
Analysis The mass flow rate of water and the rate of heat transfer to the
water are
The modified latent heat of vaporization is
The heat transfer coefficient for condensation on a single horizontal tube
is
The average heat transfer coefficient for flow inside the tube is
determined as follows:
Noting that the thermal resistance of the tube is negligible, the overall
heat transfer coefficient becomes
The logarithmic mean temperature difference is:
The tube length is determined from
Note that the flow is turbulent, and thus the entry length in this case is
10D = 0.3 m is much shorter than the total tube length. This verifies our
assumption of fully developed flow.
10-73 Saturated ammonia at a saturation temperature of Tsat = 25(C
condenses on the outer surface of vertical tube which is maintained at 15(C
by circulating cooling water. The rate of heat transfer to the coolant and
the rate of condensation of ammonia are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The tube is isothermal.
3 The tube can be treated as a vertical plate. 4 The condensate flow is
turbulentr over the entire tube (this assumption will be verified). 5 The
density of vapor is much smaller than the density of liquid, .
Properties The properties of ammonia at the saturation temperature of 25(C
are hfg = 1166(103 J/kg and (v = 7.809 kg/m3. The properties of liquid
ammonia at the film temperature of (25 + 15)/2 = 20(C are (Table A-
11),
Analysis (a) The modified latent heat of vaporization is
Assuming turbulent flow, the Reynolds number is determined from
which is greater than 1800, and thus our assumption of turbulent flow is
verified. Then the condensation heat transfer coefficient is determined
from
The heat transfer surface area of the tube is . Then the rate of heat
transfer during this condensation process becomes
(b) The rate of condensation of ammonia is determined from
10-74 There is film condensation on the outer surfaces of 8 horizontal
tubes arranged in a horizontal or vertical tier. The ratio of the
condensation rate for the cases of the tubes being arranged in a horizontal
tier versus in a vertical tier is to be determined.
Assumptions Steady operating conditions exist.
Analysis The heat transfer coefficients for the two cases are related to
the heat transfer coefficient on a single horizontal tube by
Horizontal tier:
Vertical tier:
Therefore,
10-75E Saturated steam at a saturation pressure of 0.95 psia and thus at a
saturation temperature of Tsat = 100(F (Table A-9E) condenses on the outer
surfaces of 144 horizontal tubes which are maintained at 80(F by
circulating cooling water and arranged in a 12 ( 12 square array. The rate
of heat transfer to the cooling water and the rate of condensation of steam
are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The tubes are
isothermal.
Properties The properties of water at the saturation temperature of 100(F
are hfg = 1037 Btu/lbm and (v = 0.00286 lbm/ft3. The properties of liquid
water at the film temperature of (100 + 80)/2 = 90(F are (Table A-9E),
Analysis (a) The modified latent heat of vaporization is
The heat transfer coefficient for condensation on a single horizontal tube
is
Then the average heat transfer coefficient for a 4-tube high vertical tier
becomes
The surface area for all 144 tubes is
Then the rate of heat transfer during this condensation process becomes
(b) The rate of condensation of steam is determined from
10-76E Saturated steam at a saturation pressure of 0.95 psia and thus at a
saturation temperature of Tsat = 100(F (Table A-9E) condenses on the outer
surfaces of 144 horizontal tubes which are maintained at 80(F by
circulating cooling water and arranged in a 12 ( 12 square array. The rate
of heat transfer to the cooling water and the rate of condensation of steam
are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The tubes are
isothermal.
Properties The properties of water at the saturation temperature of 10(F
are hfg = 1037 Btu/lbm and (v = 0.00286 lbm/ft3. The properties of liquid
water at the film temperature of (100 + 80)/2 = 90(F are (Table A-9E),
Analysis (a) The modified latent heat of vaporization is
The heat transfer coefficient for condensation on a single horizontal tube
is
Then the average heat transfer coefficient for a 4-tube high vertical tier
becomes
The surface area for all 144 tubes is
Then the rate of heat transfer during this condensation process becomes
(b) The rate of condensation of steam is determined from
10-77 Water is boiled at Tsat = 100(C by a chemically etched stainless
steel electric heater whose surface temperature is maintained at Ts =
115(C. The rate of heat transfer to the water, the rate of evaporation of
water, and the maximum rate of evaporation are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat losses from the
heater and the boiler are negligible.
Properties The properties of water at the saturation temperature of 100(C
are (Tables 10-1 and A-9)
" " "
Also, 0.0130 and n = 1.0 for the boiling of water on a chemically
etched stainless steel surface (Table 10-3). Note that we expressed the
properties in units specified under Eq. 10-2 in connection with their
definitions in order to avoid unit manipulations.
Analysis (a) The excess temperature in this case is which is
relatively low (less than 30(C). Therefore, nucleate boiling will occur.
The heat flux in this case can be determined from Rohsenow relation to be
The surface area of the bottom of the heater is .
Then the rate of heat transfer during nucleate boiling becomes
The rate of evaporation of water is determined from
(b) For a horizontal heating wire, the coefficient Ccr is determined from
Table 10-4 to be
Then the maximum or critical heat flux is determined from
10-78E Steam at a saturation temperature of Tsat = 100(F condenses on a
vertical plate which is maintained at 80(C. The rate of heat transfer to
the plate and the rate of condensation of steam per ft width of the plate
are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The plate is
isothermal. 3 The condensate flow is wavy-laminar over the entire plate
(this assumption will be verified). 4 The density of vapor is much smaller
than the density of liquid, .
Properties The properties of water at the saturation temperature of 100(F
are hfg = 1037 Btu/lbm and (v = 0.00286 lbm/ft3. The properties of liquid
water at the film temperature of (100 + 80)/2 = 90(F are (Table A-9E),
Analysis The modified latent heat of vaporization is
Assuming wavy-laminar flow, the Reynolds number is determined from
which is between 30 and 1800, and thus our assumption of wavy laminar flow
is verified. Then the condensation heat transfer coefficient is determined
from
The heat transfer surface area of the plate is
Then the rate of heat transfer during this condensation process becomes
The rate of condensation of steam is determined from
10-79 Saturated refrigerant-134a vapor condenses on the outside of a
horizontal tube maintained at a specified temperature. The rate of
condensation of the refrigerant is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The tube is isothermal.
Properties The properties of refrigerant-134a at the saturation
temperature of 35(C are hfg = 168.2(103 J/kg and (v = 43.41 kg/m3. The
properties of liquid R-134a at the film temperature of (35 + 25)/2 =
30(C are (Table A-10),
Analysis The modified latent heat of vaporization is
The heat transfer coefficient for condensation on a single horizontal tube
is
The heat transfer surface area of the pipe is
Then the rate of heat transfer during this condensation process becomes
The rate of condensation of steam is determined from
10-80 Saturated refrigerant-134a vapor condenses on the outside of a
horizontal tube maintained at a specified temperature. The rate of
condensation of the refrigerant is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The tube is isothermal.
Properties The properties of refrigerant-134a at the saturation
temperature of 35(C are hfg = 168.2(103 J/kg and (v = 43.41 kg/m3. The
properties of liquid R-134a at the film temperature of (35 + 25)/2 =
30(C are (Table A-10),
Analysis The modified latent heat of vaporization is
The heat transfer coefficient for condensation on a single horizontal tube
is
The heat transfer surface area of the pipe is
Then the rate of heat transfer during this condensation process becomes
The rate of condensation of steam is determined from
10-81 Saturated steam at 270 kPa pressure and thus at a saturation
temperature of Tsat = 130(C (Table A-9) condenses inside a horizontal tube
which is maintained at 110(C. The average heat transfer coefficient and the
rate of condensation of steam are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The tube is isothermal.
3 The vapor velocity is low so that Revapor < 35,000.
Properties The properties of water at the saturation temperature of 130(C
are hfg = 2174(103 J/kg and (v = 1.50 kg/m3. The properties of liquid water
at the film temperature of (130 + 110)/2 = 120(C are (Table A-9),
Analysis The condensation heat transfer coefficient is determined from
The heat transfer surface area of the pipe is
Then the rate of heat transfer during this condensation process becomes
The rate of condensation of steam is determined from
10-82 Saturated steam condenses on a suspended silver sphere which is
initially at 30(C. The time needed for the temperature of the sphere to
rise to 50(C and the amount of steam condenses are to be determined.
Assumptions 1 The temperature of the sphere changes uniformly and thus the
lumped system analysis is applicable. 2 The average condensation heat
transfer coefficient evaluated for the average temperature can be used for
the entire process. 3 Constant properties at room temperature can be used
for the silver ball.
Properties The properties of water at the saturation temperature of 100(C
are hfg = 2257(103 J/kg and (v = 0.60 kg/m3. The properties of the silver
ball at room temperature and the properties of liquid water at the average
film temperature of (100 + 40)/2 = 70(C are (Tables A-3 and A-9),
Analysis The modified latent heat of vaporization is
Noting that the tube is horizontal, the condensation heat transfer
coefficient is determined from
The characteristic length and the Biot number for the lumped system
analysis is (see Chap. 4)
The lumped system analysis is applicable since Bi < 0.1. Then the time
needed for the temperature of the sphere to rise from 30 to 50(C is
determined to be
The total heat transfer to the ball and the amount of steam that condenses
become
10-83 Steam at a saturation temperature of Tsat = 100(C condenses on a
suspended silver sphere which is initially at 30(C. The time needed for the
temperature of the sphere to rise to 50(C and the amount of steam condenses
during this process are to be determined.
Assumptions 1 The temperature of the sphere changes uniformly and thus the
lumped system analysis is applicable. 2 The average condensation heat
transfer coefficient evaluated for the average temperature can be used for
the entire process. 3 Constant properties at room temperature can be used
for the silver ball.
Properties The properties of water at the saturation temperature of 100(C
are hfg = 2257(103 J/kg and (v = 0.60 kg/m3. The properties of the silver
ball at room temperature and the properties of liquid water at the average
film temperature of (100 + 40)/2 = 70(C are (Tables A-3 and A-9),
Analysis The modified latent heat of vaporization is
Noting that the tube is horizontal, the condensation heat transfer
coefficient is determined from
The characteristic length and the Biot number for the lumped system
analysis is (see Chap. 4)
The lumped system analysis is applicable since Bi < 0.1. Then the time
needed for the temperature of the sphere to rise from 30 to 50(C is
determined to be
The total heat transfer to the ball and the amount of steam that condenses
become
10-84 Saturated steam at a saturation temperature of Tsat = 95(C (Table A-
9) condenses on a canned drink at 5(C in a dropwise manner. The heat
transfer coefficient for this dropwise condensation is to be determined.
Assumptions The heat transfer coefficient relation for dropwise
condensation that was developed for copper surfaces is also applicable for
aluminum surfaces.
Analysis Noting that the saturation temperature is less than 100(C, the
heat transfer coefficient for dropwise condensation can be determined from
Griffith's relation to be
10-85 Water is boiled at 1 atm pressure and thus at a saturation
temperature of Tsat = 100(C by a nickel electric heater whose diameter is
2 mm. The highest temperature at which this heater can operate without
burnout is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat losses from the
water are negligible.
Properties The properties of water at the saturation temperature of 100(C
are (Tables 10-1 and A-9)
" " "
Also, 0.0060 and n = 1.0 for the boiling of water on a nickel surface
(Table 10-3).
Analysis The maximum rate of heat transfer without the burnout is simply
the critical heat flux. For a horizontal heating wire, the coefficient Ccr
is determined from Table 10-4 to be
Then the maximum or critical heat flux is determined from
Rohsenow relation which gives the nucleate boiling heat flux for a
specified surface temperature can also be used to determine the surface
temperature when the heat flux is given. Substituting the maximum heat flux
into Rohsenow relation together with other properties gives
It gives the maximum temperature to be:
10-86 ... 10-93 Design and Essay Problems
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Water
1 atm
Heating wire
Ts= ?
Drink 5(C
Steam
95(C
3 cm
Ti = 30(C
Steam
100(C
Silver sphere
1.5 cm
Ti = 30(C
Steam
100(C
Silver sphere
Dtube = 3 cm
Ltube = 6 m
110(C
Condensate
Steam
270.1 kPa
Dtube = 3 cm
Ltube = 7 m
25(C
Condensate
R-134a
35(C
Dtube = 1.5 cm
Ltube = 7 m
25(C
Condensate
R-134a
35(C
Steam
100(F
Condensate
80(F
6 ft
Steam 100(C
115(C
Water, 100(C
Saturated steam
Cooling water
P = 0.95 psia
L = 15 ft
80(F
n = 144 tubes
Saturated steam
Cooling water
P = 0.95 psia
L = 15 ft
80(F
n = 144 tubes
Vertical tier
Horizontal tier
15(C
D=3.2 cm
Ltube = 2 m
Condensate
Ammonia
25(C
35(C
Cooling water
25(C
Condensate
Steam
40(C